Use trig identities to show that sec θ − cos θ = tanθ (sin θ)

Answers

Answer 1

Use [tex]\sec\theta = \dfrac{1}{\cos{\theta}}[/tex]  to get

    [tex]\sec\theta -\cos{\theta}= \dfrac{1}{\cos{\theta}}-\cos(\theta})[/tex]

Then find a common denominator:

    [tex]\dfrac{1}{\cos{\theta}}-\cos(\theta}) = \dfrac{1}{\cos{\theta}}-\dfrac{\cos^2\theta}{\cos\theta}[/tex]

But now make that one fraction:

    [tex]\dfrac{1}{\cos{\theta}}-\dfrac{\cos^2\theta}{\cos\theta} = \dfrac{1 - \cos^2\theta}{\cos{\theta}}[/tex]

But that's just sin^2 on the top

    [tex]\dfrac{1 - \cos^2\theta}{\cos{\theta}} = \dfrac{sin^2\theta}{\cos{\theta}} = \dfrac{sin\theta\cdot sin\theta}{\cos{\theta}}[/tex]

Split that fraction up:

    [tex]=\dfrac{ sin\theta}{\cos{\theta}}\cdot sin\theta[/tex]

And tan = sin/cos

    [tex]=\tan\theta\cdot sin\theta[/tex]


Related Questions


3. There are 32 students in the school play. The ratio of girls to all students
in the play is 5: 8. How many girls are in the play?
4. Two out of three vehicles in a parking lot are SUVs. There are 18 SUVs
in the parking lot. How many vehicles are in the parking lot

Answers

I believe the answers would be 20 then 27

Explanations

3- I believe the answer is 20

There are 32 students total and the ratio of girls to all of the students in the play is 5:8

So to get from 8 to 32 you need to multiply by 4, so you would go the same to the five which give you 20

The according to this, there are 20 girls in the play. And 20/32 = 62.5% as does 5/8

4- I believe the answer would be 27

As said, 2/3 of the vehicles are SUVs and that is equal to 18 SUVs.

To get what equals 1/3, you would divide 18 by two which gives you 9.

Now to get the total, you would have to multiply 9 by 3 to get all three parts which would give you 27

Please correct me if I am wrong, have a good day

what is 48% of 60? This is for Algebra 1! :)

Answers

Answer:

48% of 60 is 28.8.

48% of 60 is 28.8
hope it helps

At which value in the domain does f(x) = 0?
Ty
10
8+
6
4
2
-1
3
-10
--3

Answers

120 is the answer u neee to multy 7and 99

Expand to write an equivalent expression: -14(-8x+12y)
Factor to write an equivalent expression: 36a−16

Answers

Answer:

an equivalent expression: -14(-8x+12y)=112x-168y

factor of an equivalent expression: 36a−16=4(9a-4)

pls help with this its for math pls help

Answers

Answer:

first option

Step-by-step explanation:

divide each side by 'wh' to get:

l = V/wh

Help please anyone? ASAP!!! GIVING 15 POINTS FOR RIGHT ANSWER PLEASE

Answers

Answer:

=1.283 , 0.779 seconds

Step-by-step explanation:

h=2+33t-16t²

when h=18 ft

then18=2+33t-16t²

→ 16t²−33t+16=0  

t= [−(−33)±√{(−33) ²−4×16×16)}]/(2×16)

= [33±√{1089−1024}]/(32)

= [33±√{65}]/(32)

=1.283 , 0.779 seconds

What the first person said

Six friends attend a music concert and spend $27 per ticket. They each purchase a souvenir t-shirt. If the friends spend a total of $231, how much does each souvenir t-shirt cost

Answers

Answer:

11.50

Step-by-step explanation:

6x27=162

231+-162=69

69 divided by 6 is 11.5

11.5=11.50

11.50 is your answer

Answer:

$11.50.

Step-by-step explanation:

If there are 6 friends, and every ticket costs $27, then we need to multiply.

6 x 27 = 162.

Then, we subtract the cost of the tickets so we can find the total cost of the souvenir t-shirts.

231 - 162 = 69.

Since each of the 6 friends bought a souvenir t-shirt, we divide the total cost by the number of people.

[tex]\frac{69}{6}[/tex] = 11.5.

So, each t-shirt costs $11.50.

A cereal company puts a colored ring in each box of cereal. There are 6 different ring colors. The colors of the rings in each of 50 cereal boxes are shown in the table below. Based on the data, what is the probability that the next cereal will contain a blue or yellow ring?

Answers

the probability is unlikely OR 2/6 OR 1/3. it could be any of those! hope this helped :))

What is the answer to this question?

(3+√5)^2

Answers

Answer:

the answer to this is

14 + 6√5

14 + 6√5 because foil method

(3+√5)^2 = (3+√5)(3+√5)

3(3) = 9
3(√5) = 3√5
√5(3) = 3√5
√5(√5) = 5

9 + 3√5 + 3√5 + 5
= 14 + 6√5

At an ice cream shop, three flavors are increasing in demand. Last year, banana, pumpkin, and rocky road ice cream made up 13% of total ice cream sales. This year, the same three ice creams made up 18.1% of ice cream sales. The percentage of rocky road sales doubled, the percentage of banana sales increased by 50%, and the percentage pumpkin sales increased by 20%. If the rocky road ice cream had one less percent of sales than the banana ice cream, find out the percentage of ice cream sales each individual ice cream made last year

Answers

Answer:

Banana made=3.22

Pumpkin made=7.86

Rocky road ice cream made=1.89

Step-by-step explanation:

From the question we are told that

1st year sales(banana, pumpkin, and rocky road ice cream) [tex]S_1= 13\%[/tex]

2nd year sales:[tex]S_2=18.1\%[/tex]

Rocky road sales doubled

Banana sales increased by 50%

Pumpkin sales increased by 20%

Rocky road ice cream had one less percent then banana

Let

Banana =x

Pumpkin=y

Rocky road ice cream=z

Generally the first year equation is given mathematically as

[tex]x+y+z=13......(1)[/tex]

Generally the second year equation is given mathematically as

100% increase in Rocky road ice cream sales()z i.e double

[tex]2*z=2z[/tex]

50% increase in banana ice cream sales()x

[tex]=>1*0.50=0.5\\=>0.5+1x=1.5x[/tex]

20% increase in pumpkin(y)

[tex]=>1*0.20=0.2\\=>0.2+1x=1.2y[/tex]

Therefore second year equation is given as

[tex]1.5x+1.27y+2z=18.1.....(2)[/tex]

Generally where rocky road ice cream had one less percent of sales than the banana ice cream the equation is given as

[tex]1.5x-2z=1........(3)[/tex]

Therefore combining the three equations

x+y+z=13

1.5x+1.27y+2z=18.1

1.5x-2z=1

matrix form

[tex]\begin {bmatrix}1 & 1& 1 & 13\\1.5 & 1.2 & 2 & 18.1\\1.5 & 0 & -2 & 1\end{bmatrix}[/tex]

Generally the determinant of the first three columns

[tex]\triangle=1.8[/tex]

Solving with Crammers Rule by solving Determinant when;

Column 4 replace column 1

[tex]\triangle_1=5.8[/tex]

Column 4 replace column 2

[tex]\triangle_2=14.15[/tex]

Column 4 replace column 3

[tex]\triangle_3=3.4[/tex]

Therefore x is given my

[tex]x=\frac{\triangle_1}{\triangle}[/tex]

[tex]x=\frac{5.8}{1.8}[/tex]

[tex]x=3.22[/tex]

Therefore y is given my

[tex]y=\frac{\triangle_2}{\triangle}[/tex]

[tex]y=\frac{14.15}{1.8}[/tex]

[tex]y=7.86[/tex]

Therefore z is given my

[tex]z=\frac{\triangle_3}{\triangle}[/tex]

[tex]z=\frac{3.4}{1.8}[/tex]

[tex]z=1.89[/tex]

Therefore

Banana made=3.22

Pumpkin made=7.86

Rocky road ice cream made=1.89

The difference between 3 1/2 and 1 4/6 is _____.

A. 1 4/5
B. 2 4/5
C. 2 7/10
D. 1 7/10

Answers

Answer:

1 5/6.

Step-by-step explanation:

3 1/2 - 1 4/6

= 3 1/2 - 1 4/6

= 7/2 - 10/6        The LCM of 2 and 6 is 6 so:

= 21/6 - 10/6

= 11/6

= 1  5/6.

Find the value of x. X=​

Answers

Answer: x=9

Step-by-step explanation:

24/36=6/x

24/36=2/3

2*3=6

3*3=9

Answer:

x= 12

Step-by-step explanation:

given the f(x)=x+2 g(x)=3x²-1 what is (fg) (x)?

Answers

Answer:

(f·g)(x) = 3x² + 1

Step-by-step explanation:

Given:

f(x)=x+2,  g(x)=3x²-1

To find:

(f·g) (x) = ?

Solution:

(f·g)(x) = f(g(x)) = f(3x²-1) = (3x²-1) + 2 = 3x² + 1(f·g)(x) = 3x² + 1

7. Find the area of this trapezoid. Area =
square units. Round to the nearest whole number

1: 84
2: 119
3: 240
4: 168

Answers

A=119
119 is the answer because I solved the problem and that’s what I got so I’m probably right about the answer

Answer:

2. 119

Step-by-step explanation:

Hi guys can you answer this question​

Answers

Answer:

160403.47

Step-by-step explanation:

Please mark as brainliest

7.32*600=4392

4392*0.56= 2459.52

2459.52*3= 7378.56

7378.56/3.45=2138.71

2138.71*75= 160403.47

Answer:

28.5161739131

hope this answer helps you.....

TOP QUESTION^^ ILL GIVE BRAINLIEST

Answers

Answer:

Please read below:

Step-by-step explanation:

To calculate the area, you'll need πr². In this case, 3.14 * r²

If the radius is 50 feet, you'll calculate 50 * 3.14² which equals 492.98, or, B

Hope this helps :)

Pierson bought a stuffed bear priced at $29.95 and paid 8.5% sales tax.
What was the total cost of her purchase?

Answers

Answer:

the total cost is 32.50 or 32.49575

Step-by-step explanation:

Answer:

he payed $32.50 for the stuffed bear

Step-by-step explanation:

multiple 29.95 by.085 and then add the number you get to the original

What is the sign of 37+(-37)

Answers

Answer:

0

Step-by-step explanation:

it is neither positive nor negative.

if it helps don't forget to like and mark me

I WILL MARK BRAINLIST
At the beginning of the day the temperature was -17°C. At noon the thermometer read -2°C. What is
the total change in degrees Celsius?

Answers

Okay so to get this answer u have too Take 17 and subtract 2 This equals 15, So the answer would be 15, This is how I get my answers at least

Find the surface area of the pyramid.

Answers

Answer:

129.6

Step-by-step explanation:

A= 1/2 bh

=7.8 x 9 x 1/2

= 35.1

A= 1/2 bh

=7x 9 x 1/2

= 31.5

31.5 x 3

= 94.5

Add

35.1 + 94.5 = 129.6

Explain why this is not a polygon (10 points)

Answers

A polygon has straight sides these are curves.

А
E E
С
D
B
If mZACD = 100°, then mZACE = [?]°

Answers

Answer:

80 degrees

Step-by-step explanation:

a line is always 180 degrees

one side of that line is 100

so, just subtract 100 from 180

you get 80

180 - 100 = 80

Determine the Equation of the line Perpendicular to 2x -3y +5= 0 and passers through (-6,-3)

Answers

9514 1404 393

Answer:

  3x +2y +24 = 0

Step-by-step explanation:

In general, the equation of a perpendicular line can be found by swapping the coefficients of x and y, then negating one of them. The value of the constant will be what is required to make the line pass through the given point.

The equation will be of the form ...

  3x +2y +c = 0

At the given point, (x, y) = (-6, -3), we have ...

  3(-6) +2(-3) +c = 0 . . . . substitute the given point coordinates

  -18 -6 +c = 0 . . .simplify

  c = 24 . . . . . . . . add 24

The general-form equation for the line is ...

  3x +2y +24 = 0 . . . . . shown in blue in the attachment

Find the greatest common factor of 4c3 and 6m2.

Answers

Answer:

The GCF is 2

Step-by-step explanation:

Here, we want to find the greatest common factors of the two terms

We have the terms written in terms of the products of their multiples as follows;

4c^3 = 2 * 2 * c * c* c

6m^2 = 2 * 3 * m * m

As we can see, the greatest common factor of the two is simple the value 2

Find the volume

A. 150 cm3

B. 180 cm3

C. 90 cm3

D. 90 cm2

Answers

Answer:

268 in²

Step-by-step explanation:

The surface area is basically the entire area of the figure. You can do it multiple ways, but this is how I did it. I found the area of each side and added them all together. There are three sets of identical sides. First, we'll calculate the area of the side with lengths 10" and 8".

10 · 8 = 80

There are two of these sides, so currently we have 80 + 80.

Next, the area of the sides with lengths 8" and 3". These are the sides at the top and bottom.

8 · 3 = 24

So to our equation we now have 80 + 80 + 24 +24.

For the final two sides, we have the dimensions 10" and 3".

10 · 3 = 30

To our equation, we add this to get 80 + 80 + 24 + 24 + 30 +30.

Add all these numbers together for 268.

In the correct form, we add the square symbol to show that we are talking about area. The answer is 268 in². Good luck :D

need help plz.......

Answers

Answer:

oh I see. that's an interesting question but the problem is I hate maths

What is a correct name for the angle shown? R S T O LE O ZS O LEITE O LEFT​

Answers

Answer:

RTS.

Step-by-step explanation:

This is an obtuse angle.

How does Momma act differently when she is with her mother in Alabama compared to how she acts at home in Flint? plz i will gave brainest

Answers

Answer:Watson act differently when she is with her mother in Alabama compared with how she acts at home in Flint? Mrs. Watson acts calm in front of her Mother. In Flint, Mrs.

Step-by-step explanation:

Erica's bill for breakfast at a restaurant was $64. She left an 18% tip. What was the amount of the tip?

Answers

Answer:

$11.52

Step-by-step explanation:

18% of 64 is 11.52

How much money will there be in an account at the end of 10 years if $3000 is deposited at 3% interest compounded
semi-annually? (Assume no withdrawals are made. Use the formula A=P
-p(1-4)
for compound interest,

Answers

Answer:

$4040.57

Step-by-step explanation:

A=P(1+(r/n))^nt

P = Principal = 3000

r = rate = 0.03

n = no. times payed each year = 2

t = years = 10

A = 3000(1 + (0.03/2))^(2x10)

A = 3000(1.015)^20

A = 4040.57 (2.d.p)

Hope this helped!

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